Technique for stimulating the emission of far-infrared radiation

ABSTRACT

There is disclosed a method and an apparatus for stimulating the emission of far-infrared optical radiation by backscattering microwaves from a relativistic electron beam having energy in the 1 to 10 Megaelectron-volt range and having direction along a magnetic field of magnitude chosen to make the electron cyclotron frequency approximately equal to the microwave frequency and by resonating the scattered radiation. A van de Graaf generator generates the electron beam.

I United States Patent 1131 3,639,774 Wolff Feb. 1, 1972 I 1 TECHNIQUE FOR STIMULATING THE 3,230,466 1/1966 Brett a 111 ..33o/s3 EMISSION OFFAR-INFRARED 3,398,376 8/1968 Hirshfield ..330/$6 RADIATION P E John K'nsk' 72 Inventor: Peter Adalbert wan, Berkeley 1161 1116,,f,",',,,'-;', ,,";f J

Attorney-R. J. Guenther and Arthur J. Torsiglieri [73] Assignee: BellTelephone Laboratories, Incorporated,

Murray Hill, NJ. 57] CT [22] Filed: July 24, 1970 l There is disclosed amethod and an apparatus for stimulating [21] the emission offar-infrared optical radiation by backscattering microwaves from arelativistic electron beam having ener- 52] us. (:1. ..307l88.3, 321/69R ay in the 1 to lo Mevelectron-volt s a i g irec n [51] Int. Cl. .11037/00 along a gn fi f manit chosen t m ke h le [58] Field of Search..307/88.3; 321/69 tron cyclotron frequency approximately equal to themicrowave frequency and by resonating the scattered radia- [S6]Relerenees Cited tion. A van de Graaf generator generates the electronbeam.

UNITED STATES PATENTS 8 l 3,177,435 4/1965 M Marcuse 33Q/QQ T SOURCE OFVARIABLE /l7 OPTICAL CURRENT RESONATOR SOLENOID l3 IIIIIIMIIAIIII 6 16VAN DE GRAAF GENERATOR 2 l4 BACKSCATTERED FAR INFRARED BEAM 12TRAVELLING WAVE MICROWAVE CAVITY H MIC ROWAV E SOURCE PHASED FEED PORTSv TECHNIQUE FOR STIMULATING THE EMISSION OF FAR-INFRARED RADIATIONBACKGROUND OF THE INVENTION This invention relates to a method and anapparatus for stimulating the emission of radiation, particularlyfar-infrared optical radiation.

It is well known that optical techniques provide a powerful tool for thestudy of matter. In addition, the development of the laser and relatedsources of coherent radiation has generated great interest both in theproperties of optical radiation fields and in a wide variety of possibleapplications of such fields. These applications include communication.

Yet, despite these facts, there remains an important region of theoptical spectrum in which sources of radiation are generally feeble andin which experiments are exceedingly difficult to perform. This regionis part of the far infrared and lies between a wavelength of the orderof a millimeter and a wavelength of about 50 micrometers. Some yearsago, this portion of the spectrum was nearly unexplored. Since then, thedevelopment of Fourier transform spectroscopy, which makes optimal useof weak sources, and the invention of devices such as the carcinatron,the hydrogen cyanide (HCN) laser and the water vapor laser have made itmore accessible. Also, very recently, optically pumped lasers such asthe methyl fluoride laser disclosed in the copending patent applicationof T. Chang et al., Ser. No. 24,703, filed Apr. 1, 1970, and assigned tothe assignee hereof, have been invented. Nevertheless, it remains truethat sources of radiation in the far infrared between 100 micrometersand 1,000 micrometers, particularly tunable ones, are inadequate.

SUMMARY OF THE INVENTION I have invented a method for generating amoderately intense, continuously tunable, coherent source of radiationin this wavelength range. The method of my invention comprises the stepsof directing a relativistic electron beam along a magnetic field thatmakes the cyclotron frequency of electrons therein equal to a suppliedmicrowave frequency seen by the electron in its rest frame, supplyingcoherent microwave energy to said beam at said frequency to producebackscattered radiation from said beam at a different frequency, andmeans for resonating said backscattered radiation to produce thestimulated emission of radiation at said different frequency.

More specifically, the method according to my invention includesbackscattering microwaves from a relativistic electron beam having asubstantially uniform electron energy in the l to Megaelectron-voltrange and having direction along a magnetic field of magnitude chosen tomake the electron cyclotron frequency approximately equal to themicrowave frequency and include resonating the scattered radiation. Thecoincidence of frequencies provides a type of antiStokes scatteringwhich can be characterized as resonant Thomson scattering, although suchscattering has never before been proposed for a moving electron beam.

BRIEF DESCRIPTION OF THE DRAWING Further features and advantages of myinvention will become apparent from the following detailed description,taken together with the drawing, in which the sole FIGURE is a partiallypictorial and partially schematic illustration of the preferredembodiment of the invention.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENT In the embodiment of the drawing,it is desired to obtain a moderately intense, continuously tunable,coherent source of radiation in the far infrared from a source ofmicrowaves at much longer wavelength. The microwave source is shown assource 11 in the drawing. This source is coupled to a traveling wavemicrowave cavity 12 at the ports 11A and [1B, which phase the microwavesfrom source 11 to launch a traveling wave to the right in cavity 12. Inthe upper arm of cavity 12 the microwave field is propagating to theleft through a region surrounded by a solenoid 13, while a relativisticelectron beam propagates to the right from a van de Graaf generator 14along the axis of the solenoid l3. Suitable windows 15 and I6 areprovided in the ends of the upper arm of the microwave cavity in orderto permit the backscattered far-infrared radiation to pass therethroughbetween the reflectors l7 and 18 of a resonator for the far-infraredradiation.

While the microwave field could be injected into the apparatus from theright without being guided by the cavity 12, confinement of themicrowave field in this manner facilitates its efficient utilization.Higher fields result for a given input power because of the cavity.Also, it may be feasible to substitute some other source of high-energyelectrons for the van de Graaf generator 14; but the van de Graafgenerator 14 is definitely preferred at the present time because of thenarrow energy range it permits to electrons in the beam transmitted fromit. A relatively narrow electron energy range is highly desirable, eventhough it is desirable to be able to change this energy along with themagnetic field to achieve tuning. The van de Graaf generator providesthis capability. It should be understood that the solenoid 13 is readilyenergized from a source 19 of variable current.

The operation of my invention can be described briefly as follows. Theincrease in frequency of the scattered radiation with respect to theincident radiation is a Doppler shift upwards in frequency because theelectron beam and the supplied microwave field are propagating inantiparallel directions.

A more detailed and mathematical description follows.

The basic technique of anti-Stokes backscattering has previously beenused to generate X-rays by backscattering a ruby laser beam from highlyrelativistic electrons, as described in the article by H. H. Bingham etal., Physical Review Letters, Vol. 23, page 498 (Sept. 1, 1969). In suchexperiments, however, the X-ray beam is produced by spontaneousscattering. Therefore, it is relatively weak and incoherent. Bycontrast, I have recognized that with microwave excitation and resonantscattering it is feasible to attain stimulated anti-Stokesbackscattering.

Several factors combine to reduce the stimulated scattering threshold toa reasonable value in the far-infrared range. Perhaps most important isthe well-known fact that the threshold for stimulated scattering at afrequency w, varies inversely with the density of electromagnetic modesat this frequency, that is, as wf. This factor greatly favorslow-frequency scattering such as that we are considering. Secondly, inthe microwave region exceedingly powerful sources are available toprovide the electromagnetic field which is backscattered; their photonfluxes can be further increased by the use of high Q cavities orresonators.

Finally, with microwave or far-infrared excitation, it is possible toenhance greatly the electron photon scattering cross section by using aform of resonance. This enhancement is achieved by performing thescattering in a magnetic field aligned parallel to the electronpropagation direction. The magnitude of this field is chosen to make theelectron cyclotron frequency approximately equal to the microwavefrequency, as seen in the electron rest frame of reference. Under suchconditions, there is a large enchancement of the electron-photonscattering cross section. This effect is a form of resonantfluorescence. It has sometimes been called magneto-Thompson scattering.Under reasonable experimental conditions, the resonant enhancement canprovide as much as a millionfold increase of the scattering crosssection over the nonresonant value.

It is reiterated, for emphasis, that this enhancement of cross section,as well as the other favorable factors mentioned above, are all requiredto achieve a reasonable value of the threshold for stimulatedbackscattering.

KINETICS OF ELECTRON SCATTERING The essential features of the operationof the machine we propose will now be discussed in more detail withreference to the drawing. Here, a moderately relativistic electron beam(energy 1-1 Mev.) travels in the +2 direction, and intercepts anoppositely directed microwave beam. The interaction region is in auniform, z-directed magnetic field whose value is adjusted to achievecyclotron resonance. Some of the photons are backscattered from theelectron beam into the +2 direction. Their final energy is higher thanthat of the incident photons because of the Doppler effect. Themagnitude of this frequency shift can easily be estimated. In thetransformation to the electron rest frame, the photon energy isincreased by the factor where (n is the frequency of the incidentphoton, m, is the photon frequency in the electron rest frame, B=vlcwhere v is the electron velocity, and y=(l-B)""". The photon w (whoseenergy is small compared to me) scatters essentially elastically in thiscoordinate system. After transforming back to the laboratory frame, onefinds that the frequency of backscattered photons is J a)='y +B) +B/ B)(2) For electrons whose energies are appreciably greater than me,equation (2) can be rewritten in the form:

o)=-( /m (3) where'E is the total electron energy. This formulaindicates, for example,that electrons of about 8 Mev. are required tofrequency shift lO-cm. microwaves to the lOO-micrometer range (m,/w,,=l,000).

It is also important to consider the angular distribution anddifferential cross section of the scattering. In the electron restframe, the distribution is the well-known dipole scattering intensitywith a differential cross section d0'/dO='-(e /mc for backscattering.This distribution becomes sharply peaked in the +1 direction when onetransforms to the laboratory frame. The effect is a purely kinematicone, resulting from the fact that a scattering angle 0, in the restframe transforms into a scattering angle in the laboratory frame (thisresult valid for 0, l The upshot is an enhancement of the cross sectionfor backscattering in the laboratory frame by a factor (1 [3/ l ascompared to the electron rest frame. Thus, in the laboratory frame, thedifferential cross section for backscattering is do' 1+ ,B e 2 r (i s)(a Equation (4) applies when there is no magnetic field (B=O).

In the presence of a field, the cross section is enhanced by cyclotronresonance. The optimal case is that in which the fields are circularlypolarized in such a way as to couple to that electrons cyclotron motion.A simple calculation then shows that, for the geometry we areconsidering, the differential cross section for backscattering becomes d'(1fl) (w. w.)

where w,=eB/mc is the electron cyclotron frequency and in, (see equation(1)) is the frequency seen by the electron in its rest frame. This isthe expression we will use in estimating Raman gain, below. To myknowledge, the resonant enhancement of light scattering via cyclotronresonance described by equation (5) has not been discussed in sufficientdetail in the literature, though the effect is fairly well known, aphenomenon which may be termed magneto-Thomson scattering." See theProceedings of the Ninth International Conference an the Physics ofSemiconductors, (Moscow) Publishing House Nuukn," Leningrad I968) in thepaper by B. Lax. at page 253.

Finally, we estimate the magnetic field strengths required to achievecyclotron resonance in the electron rest frame (w,= (u For the examplediscussed above (AD Zwc/w I 0 cm., M lrrclail fi ofi) brie finds thatcyclotron fesonahce is achieved if B 40 kilogauss. Such fields are nowreadily attainable with superconducting solenoids. Lower electronenergies and lower fields are, of course, required to produce scatteredwavelengths (and resonance) at longer wavelengths than micrometers.

RAMAN GAIN Using the formulas and concepts of the preceding section, wecan now derive an expression for the Raman gain. This quantity isdefined as the logarithmic derivative of the scattered photon intensitywith respect to distance. It is also equal to l/c Xthe net rate ofphoton scattering per mode of the scattered field). in calculating thisscattering rate, one must take account of the fact that both forward(w,,- w.) and reverse (to, (0,) scattering processes can occur. The gainis determined by their difference, which is much smaller than theindividual forward or reverse processes. This effect leads to' a termsimilar to the usual Boltzmann factor in the expression for the Ramangain.

It is important, in discussing this problem, to specify the velocity (ormomentum) distribution of the electrons which cause the scattering. Wewill assume that they have an average momentum, p (with correspondingvelocity v) and a small spread, Ap (Ap about this average value. Theseare components of momentum. Transverse momenta will be ignored, sincethey only produce a small, second-order Doppler shift.

Let us now focus our attention on scattering processes in which a photonof frequency m backscatters to energy (0,. This frequency shift isproduced by those electrons with velocity B=( u/ 0) 6) a result which isobtained by rewriting equation (2). The corresponding momentum is Ofcourse, for appreciable scattering to occur at frequency (0,,

there must be some electrons with momentum p,, i.e., p must be fairlyclose to p. However, we do not require that p =p exactly. As theseelectrons scatter light, they recoil to a new momentum where k,=w,/c.Thus, we obtain the following expression for assesses; m. mp.) {can};(1)? where N is the photon flux (at frequency m y'and n the electrondensity in the interaction region. This expression assumes thatf(p,) isnormalized:

Since 1 p,) is small, one may approximate (if hk. FI (l2) Finally, forrelativistic electrons, AE cAp, where AE is the energy spread of theelectron beam. Combining equations (l), (l2), and 13) yields thefollowing formula for the gain:

1 2 e 2 fin), me 0 =2 i (Fa) (m) X (Xi) (E) where A, is the wavelengthof the photons in the electron rest frame. Equation (14) is the majorresult of this analysis. It has here been derived in a rather intuitiveway. However, a detailed calculation, proceeding from the Boltzmannequation, of the third order optical nonlinearity which is responsiblefor stimulated Raman scattering, confirms equation (14). Since thiscalculation is quite lengthy, and follows standard lines, it will not bepresented here.

It is important to notice that, in equation 14), G varies as (AE) Thus,monochromaticity of the electron beam is a crucial requirement inachieving stimulated magneto-Thomson scattering.

We calculate the gain that might be achieved under reasonableexperimental conditions as follows. For this estimate we have used thefollowing parameters: (m,/w,-w,)=l0 this requires a field homogeneity of0. 1 percent.

AE=i ,000 ev.

Beam current--10 amp/cm.

A =10 cm.

Microwave power= l kw./cm.

(N,,=X l 0 photons/cm. sec.

With these numbers, the gain calculated from equation i4) is about 5X10emf. If the interaction region between the electron and microwave beamsis cm. long, CW Raman laser action can be achieved if the scattered lRlight is confined within a resonator l7, 18 whose mirrors have 97.5percent reflectivity. Such cavities can certainly be built.

The figures for microwave power, beam current, energy definition andfield homogeneity assumed above all seem within the present state of theart. The most difficult to achieve is the electron beam current of lmilliamp (at several Mev.) with an energy spread of 1,000 ev. or less.Such beams can probably be obtained from a well-stabilized van de Graaf.However, it would be very useful to be able to relax theserequirementsparticularly as to beam current. Smaller electron beamcurrents and/or poorer energy definition could be compensated byincreasing the microwave photon flux, N A convenient way to do thismight be with a traveling wave cavity, as illustrated schematically inthe drawing. Here the electron beam passes through holes in the cavity,scattering from the circulating microwave fields. A traveling wavecavity is required to insure that the microwave radiation has awelldefined wave vector. This condition is necessary since the Dopplershift is related to the wave vector.

The advantage of the geometry illustrated in the drawing is that themicrowave cavity 0 can be used to enhance the circulating microwavepower, without a corresponding increase in input power. At roomtemperature Q=l00 is not unreasonable; higher Qs might be obtained atlow temperatures.

The preceding calculations suggest that CW, stimulated Raman scatteringof microwave photons from a relativistic electron beam is achievable.Though our estimates of Raman gain are encouraging, it seems prematureat this time to attempt a detailed design of the CW device. A morefruitful approaeh is probably to test the basic idea-particularly theconcept of magnetic field enhancement of the cross section-in a pulsedexperiment. Microwave powers exceeding a megawatt, and much largerelectron beam currents than those we have visualized, are attainable inpulsed operation. These high powers would permit considerable relaxationof the restriction on electron energy spread (AE=1,000 ev.) and thecondition on magnetic field homogeneity required to maintain cyclotronresonance (AB/BA 0' lelaim:

l. A method for stimulating the emission of radiation, comprising thesteps of supplying an electron beam aligned with a magnetic field makingthe cyclotron frequency of electrons therein equal to a first frequency,supplying coherent microwave energy to said beam at substantially saidfirst frequency to produce backscattered radiation from said beam at adifferent frequency, and resonating said backscattered radiation toproduce the stimulated emission of said radiation at said differentfrequency.

2. A method according to claim 1 in which the electron beam-supplyingstep comprises supplying the electron beam with a substantially uniformelectron energy lying in the range between 1 and 10 Megaelectron volts.

3. A method according to claim 2 in which the microwave energy-supplyingstep comprises guiding the microwave energy in a traveling waveform topropagate substantially antiparallel to and substantially collinearlywith the electron beam throughout a selected pathlength of said beam.

4. A method according to claim 3 in which the guiding step includesresonating said microwave energy in said traveling waveform.

5. An apparatus for stimulating the emission of radiation, comprisingmeans for establishing a magnetic field,

means for supplying an electron beam in which electrons have substantialkinetic energies of nearly equal values and velocities collinear withsaid field,

means for supplying coherent microwave energy to said beam at afrequency substantially equal to the cyclotron frequency of saidelectrons in said magnetic field to produce backscattered radiation fromsaid beam at a dif-- 6. An apparatus according to claim 5 in which theelectron beam-supplying means comprises a van de Graaf generatorsupplying the electron beam with substantially uniform electron energylying in the range between 1 and 10 Megaelectron volts.

7. An apparatus according to claim 6 in which the microwaveenergy-supplying means comprises a loop-type traveling wave microwaveresonator including openings for passing the electron beam and thescattered radiation, said microwave energy-supplying means includingmeans for launching said microwave energy in said resonator to propagateantiparallel to said electron beam while substantially collineartherewith.

8. An apparatus according to claim 7 in which the microwaveenergy-launching means launching microwave energy having a wavelengthbetween about 2 and 20 centimeters and the means for establishing amagnetic field includes a frequency.

1. A method for stimulating the emission of radiation, comprising thesteps of supplying an electron beam aligned with a magnetic field makingthe cyclotron frequency of electrons therein equal to a first frequency,supplying coherent microwave energy to said beam at substantially saidfirst frequency to produce backscattered radiation from said beam at adifferent frequency, and resonating said backscattered radiation toproduce the stimulated emission of said radiation at said differentfrequency.
 2. A method according to claim 1 in which the electronbeam-supplying step comprises supplying the electron beam with asubstantially uniform electron energy lying in the range between 1 and10 Megaelectron volts.
 3. A method according to claim 2 in which themicrowave energy-supplying step comprises guiding the microwave energyin a traveling waveform to propagate substantially antiparallel to andsubstantially collinearly with the electron beam throughout a selectedpathlength of said beam.
 4. A method according to claim 3 in which theguiding step includes resonating said microwave energy in said travelingwaveform.
 5. An apparatus for stimulating the emission of radiation,comprising means for establishing a magnetic field, means for supplyingan electron beam in which electrons have substantial kinetic energies ofnearly equal values and velocities collinear with said field, means forsupplying coherent microwave energy to said beam at a frequencysubstantially equal to the cyclotron frequency of said electrons in saidmagnetic field to produce backscattered radiation from said beam at adifferent frequency, and means for resonating said backscatteredradiation to produce the stimulated emission of said radiation at saiddifferent frequency.
 6. An apparatus according to claim 5 in which theelectron beam-supplying means comprises a van de Graaf generatorsupplying the electron beam with substantially uniform electron energylying in the range between 1 and 10 Megaelectron volts.
 7. An apparatusaccording to claim 6 in which the microwave energy-supplying meanscomprises a loop-type traveling wave microwave resonator includingopenings for passing the electron beam and the scattered radiation, saidmicrowave energy-supplying means including means for launching saidmicrowave energy in said resonator to propagate antiparallel to saidelectron beam while substantially collinear therewith.
 8. An apparatusaccording to claim 7 in which the microwave energy-launching meanslaunching microwave energy having a wavelength between about 2 and 20centimeters anD the means for establishing a magnetic field includes avariable current source capable of varying said field to maintain theelectron cyclotron frequency equal to the microwave frequency.